few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Topic options: 
A. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
B. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
C. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
D. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
E. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
F. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
G. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
H. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
I. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
J. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
K. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.


Thought: This problem teaches students different ways of writing numbers that express the same value. This helps students better understand the complex number system, which includes rational numbers.
Answer: I

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001097

7
options: Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
problem_activity: Narrative
The purpose of this activity is to give students a concrete experience of building the boundary of shapes and quantifying that length of the boundary, allowing them to conceptualize perimeter as a measurable geometric attribute. Students use
\(1\frac{1}{4}\)
-inch paper clips as the units for measuring the distances around four shapes. The reasoning here prepares them to reason about equal-size intervals that can be marked on the sides of a shape to measure its length (as students will see in the next activity).
Required Materials
Materials to Gather
Paper clips
Materials to Copy
What Does It Take to Build the Shapes?
Required Preparation
Each group of 4 needs 25-50 paper clips that are
\(1\frac{1}{4}\)
-inch long each.
If using 1-inch paper clips, use 80% scale when making copies of the blackline masters.
Launch
Groups of 4
Give each group a copy of the blackline master and 25–50 paper clips.
“Make a prediction: Which shape do you think will take the most paper clips to build?”
30 seconds: quiet think time
Poll the class on whether they think shape A, B, C, or D would take the most paper clips to build.
Activity
“Work with your group to find out which shape takes the most paper clips to build. You may need to take turns with the paper clips.”
5–7 minutes: small-group work time
Monitor for students who:
place paper clips one at a time and then count the total
place paper clips one at a time and then add up the numbers on all sides
use multiplication (
\(3 \times 3\)
for B,
\((2 \times 4) + (2 \times 2)\)
for C, or
\((2 \times 6) + 2\)
for D)
use estimation
Student Facing
Your teacher will give you four shapes on paper and some paper clips.
Work with your group to find out which shape takes the most paper clips to build. Explain or show how you know. Record your findings here. Draw sketches if they are helpful.
A
B
C
D
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Select previously identified students to share their responses and strategies for finding the number of paper clips. Record the different strategies for all to see.
“What we have done in this activity is to find the length of the boundary of shapes. The boundary of a flat shape is called its
perimeter
.”
“When we find the distance all the way around a shape, like we did with paper clips, we are measuring its perimeter.”
“To find the length of the perimeter of a shape, we can find the sum of its side lengths.”
“We can say that the perimeter of shape A is 13 paper clips long.”
“When we say ‘find the perimeter,’ we mean find the length of the perimeter.”


correct_option_index: 2